time results from the manner in which the Jacobian matrix for the

Newton-Raphson step is computed. Each column is computed by perturbing

one of the variables and re-solving the Gauss-Seidel equations to

determine the change in the functions VT and VE. An algebraic substi-

tution to eliminate all Gauss-Seidel variables, as suggested by Orbach

et al. (1972), would greatly reduce the computational effort required.


7.3 Discussion

 The same set of equations was used for the analysis of both

problems. The equations were written so that the only possible output

of the bubble point equations, Q, was temperature. This is compatible

with the methods traditionally used to solve distillation problems with

components having a narrow range of boiling points. When a system

having a wide range of boiling points is encountered, it is common

practice to rewrite the equations so that the temperature is calculated

in an enthalpy balance equation. This was not done fo' the second

problem and GENIE generated a Gauss-Seidel solution procedure for that

problem. In checking the solution procedure, however, it was found to

be non-convergent. The solution procedure was modified, by combining

the Newton-Raphson method with the Gauss-Seidel, to improve its

convergence characteristics. The new solution procedure was found to be

convergent.

 The presence of extremely large eigenvalues for the convergence

matrix, as wras the case for the second problem, can he an indication to

the engineer that an algebraic re-arrangement of his model is in order.

By examining the expanded coefficient matrix and noLing which non-output

terms are much larger than output terms, he can discover the cause of